Problems 401 to 500

Table 4.853: First order ode non-linear in derivative


#	ODE	Mathematica	Maple	Sympy

5655	\[ {} {y^{\prime }}^{6} = \left (y-a \right )^{4} \left (y-b \right )^{3} \]	✓	✓	✓

5656	\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3} = 0 \]	✓	✓	✓

5657	\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3} = 0 \]	✓	✓	✓

5658	\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4} = 0 \]	✓	✓	✗

5659	\[ {} x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2} \]	✗	✗	✗

5660	\[ {} 2 \sqrt {a y^{\prime }}+x y^{\prime }-y = 0 \]	✓	✓	✓

5661	\[ {} \left (x -y\right ) \sqrt {y^{\prime }} = a \left (1+y^{\prime }\right ) \]	✓	✓	✓

5663	\[ {} \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } = x \]	✓	✓	✓

5664	\[ {} \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } = y \]	✓	✓	✓

5665	\[ {} \sqrt {1+{y^{\prime }}^{2}} = x y^{\prime } \]	✓	✓	✓

5666	\[ {} \sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+x y^{\prime }-y = 0 \]	✓	✓	✗

5667	\[ {} a \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \]	✓	✓	✗

5668	\[ {} a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \]	✓	✓	✓

5669	\[ {} \sqrt {\left (a \,x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )}-y y^{\prime }-a x = 0 \]	✓	✓	✓

5670	\[ {} a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+x y^{\prime }-y = 0 \]	✓	✓	✗

5671	\[ {} \cos \left (y^{\prime }\right )+x y^{\prime } = y \]	✓	✓	✗

5672	\[ {} a \cos \left (y^{\prime }\right )+b y^{\prime }+x = 0 \]	✓	✓	✗

5673	\[ {} \sin \left (y^{\prime }\right )+y^{\prime } = x \]	✓	✓	✗

5674	\[ {} y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right ) = y \]	✓	✓	✗

5675	\[ {} {y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right ) = y \]	✓	✓	✗

5676	\[ {} \left (1+{y^{\prime }}^{2}\right ) \sin \left (x y^{\prime }-y\right )^{2} = 1 \]	✓	✓	✗

5677	\[ {} \left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime } = 0 \]	✓	✓	✗

5678	\[ {} {\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✗

5679	\[ {} \ln \left (y^{\prime }\right )+x y^{\prime }+a = 0 \]	✓	✓	✓

5680	\[ {} \ln \left (y^{\prime }\right )+x y^{\prime }+a = y \]	✓	✓	✓

5681	\[ {} \ln \left (y^{\prime }\right )+x y^{\prime }+a +b y = 0 \]	✓	✓	✓

5682	\[ {} \ln \left (y^{\prime }\right )+4 x y^{\prime }-2 y = 0 \]	✓	✓	✓

5683	\[ {} \ln \left (y^{\prime }\right )+a \left (x y^{\prime }-y\right ) = 0 \]	✓	✓	✓

5684	\[ {} a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y = 0 \]	✓	✓	✓

5685	\[ {} y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0 \]	✓	✓	✓

5686	\[ {} y^{\prime } \ln \left (y^{\prime }\right )-\left (1+x \right ) y^{\prime }+y = 0 \]	✓	✓	✗

5687	\[ {} y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0 \]	✓	✗	✗

5688	\[ {} \ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y \]	✓	✓	✗

5696	\[ {} y^{2} \left (1+{y^{\prime }}^{2}\right ) = R^{2} \]	✓	✓	✓

5697	\[ {} y = x y^{\prime }+\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \]	✓	✓	✗

5698	\[ {} y = x {y^{\prime }}^{2}+{y^{\prime }}^{2} \]	✓	✓	✓

5750	\[ {} {y^{\prime }}^{2}-5 y^{\prime }+6 = 0 \]	✓	✓	✓

5751	\[ {} {y^{\prime }}^{2}-\frac {a^{2}}{x^{2}} = 0 \]	✓	✓	✓

5752	\[ {} {y^{\prime }}^{2} = \frac {1-x}{x} \]	✓	✓	✓

5753	\[ {} {y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1 = 0 \]	✓	✓	✗

5754	\[ {} y = a y^{\prime }+b {y^{\prime }}^{2} \]	✓	✓	✓

5755	\[ {} x = a y^{\prime }+b {y^{\prime }}^{2} \]	✓	✓	✓

5756	\[ {} y = \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \]	✓	✓	✓

5757	\[ {} x = \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \]	✓	✓	✓

5758	\[ {} y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x} = 0 \]	✓	✓	✓

5759	\[ {} x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2} = 0 \]	✓	✓	✓

5760	\[ {} 1+{y^{\prime }}^{2} = \frac {\left (x +a \right )^{2}}{2 a x +x^{2}} \]	✓	✓	✓

5761	\[ {} y = x y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \]	✓	✓	✓

5762	\[ {} y = x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \]	✓	✓	✗

5763	\[ {} y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✓

5764	\[ {} y = x y^{\prime }+a x \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✓

5765	\[ {} x -y y^{\prime } = a {y^{\prime }}^{2} \]	✓	✓	✗

5766	\[ {} x +y y^{\prime } = a \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

5767	\[ {} y y^{\prime } = x +y^{2}-y^{2} {y^{\prime }}^{2} \]	✓	✓	✓

5768	\[ {} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \]	✓	✓	✓

5769	\[ {} y-2 x y^{\prime } = x {y^{\prime }}^{2} \]	✓	✓	✓

5770	\[ {} \frac {y-x y^{\prime }}{y^{2}+y^{\prime }} = \frac {y-x y^{\prime }}{1+x^{2} y^{\prime }} \]	✓	✓	✓

6027	\[ {} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \]	✓	✓	✗

6028	\[ {} {y^{\prime }}^{2} \left (-x^{2}+1\right )+1 = 0 \]	✓	✓	✓

6571	\[ {} y = x y^{\prime }+{y^{\prime }}^{4} \]	✓	✓	✗

6666	\[ {} x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0 \]	✓	✓	✓

6667	\[ {} x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-x \left (-1+y\right ) = 0 \]	✓	✓	✓

6668	\[ {} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2} = 0 \]	✓	✓	✓

6669	\[ {} 3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \]	✓	✓	✓

6670	\[ {} 8 y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \]	✓	✓	✗

6671	\[ {} y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \]	✓	✓	✗

6672	\[ {} {y^{\prime }}^{2}-x y^{\prime }+y = 0 \]	✓	✓	✓

6673	\[ {} 16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \]	✓	✓	✗

6674	\[ {} x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y = 0 \]	✓	✓	✗

6675	\[ {} x {y^{\prime }}^{2}-y y^{\prime }-y = 0 \]	✓	✓	✗

6676	\[ {} y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \]	✓	✓	✗

6677	\[ {} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \]	✓	✓	✗

6678	\[ {} y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2} \]	✓	✓	✓

6679	\[ {} y = 2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✓

6680	\[ {} y {y^{\prime }}^{2}-x y^{\prime }+3 y = 0 \]	✓	✓	✓

6681	\[ {} y = x y^{\prime }-2 {y^{\prime }}^{2} \]	✓	✓	✓

6682	\[ {} y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \]	✓	✓	✗

6683	\[ {} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2} = 0 \]	✓	✓	✓

6684	\[ {} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0 \]	✓	✓	✓

6685	\[ {} \left (3 y-1\right )^{2} {y^{\prime }}^{2} = 4 y \]	✓	✓	✗

6686	\[ {} y = -x y^{\prime }+x^{4} {y^{\prime }}^{2} \]	✓	✓	✓

6687	\[ {} 2 y = {y^{\prime }}^{2}+4 x y^{\prime } \]	✓	✓	✗

6688	\[ {} y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y \]	✓	✓	✓

6689	\[ {} {y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0 \]	✗	✓	✗

6690	\[ {} \left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2} = \left (x +y y^{\prime }\right )^{2} \]	✓	✓	✗

6883	\[ {} \sin \left (y^{\prime }\right ) = x +y \]	✓	✓	✓

6884	\[ {} \sin \left (x^{\prime }\right )+y^{3} x = \sin \left (y \right ) \]	✗	✗	✗

6918	\[ {} {y^{\prime }}^{2} = 4 y \]	✓	✓	✓

6919	\[ {} {y^{\prime }}^{2} = 9-y^{2} \]	✓	✓	✗

6921	\[ {} {y^{\prime }}^{2}-2 y^{\prime }+4 y = 4 x -1 \]	✓	✓	✗

6928	\[ {} x {y^{\prime }}^{2}-4 y^{\prime }-12 x^{3} = 0 \]	✓	✓	✓

6994	\[ {} {y^{\prime }}^{2} = 4 x^{2} \]	✓	✓	✓

7005	\[ {} 1+{y^{\prime }}^{2} = \frac {1}{y^{2}} \]	✓	✓	✓

7132	\[ {} {y^{\prime }}^{2}+y^{2} = 1 \]	✓	✓	✓

7137	\[ {} 1+{x^{\prime }}^{2} = \frac {a}{y} \]	✓	✓	✓

7439	\[ {} y^{\prime } \left (y^{\prime }+y\right ) = x \left (x +y\right ) \]	✓	✓	✓

7440	\[ {} \left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime } \]	✓	✓	✓

7441	\[ {} x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2} = 0 \]	✓	✓	✓

7443	\[ {} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \]	✓	✓	✗

7514	\[ {} x +y y^{\prime } = a {y^{\prime }}^{2} \]	✓	✓	✗

4.14.5 Problems 401 to 500