Problems 4101 to 4200

Table 4.83: First order ode


#	ODE	Mathematica	Maple	Sympy

8731	\[ {} y^{\prime } = \sqrt {1-x^{2}-y^{2}} \]	✗	✗	✗

8732	\[ {} y^{\prime }+\frac {y}{3} = \frac {\left (1-2 x \right ) y^{4}}{3} \]	✓	✓	✓

8733	\[ {} y^{\prime } = \sqrt {y}+x \]	✓	✓	✗

8734	\[ {} y^{2}+x^{2} y^{\prime } = x y y^{\prime } \]	✓	✓	✓

8735	\[ {} y = x y^{\prime }+x^{2} {y^{\prime }}^{2} \]	✓	✓	✓

8736	\[ {} \left (x +y\right ) y^{\prime } = 0 \]	✓	✓	✓

8737	\[ {} x y^{\prime } = 0 \]	✓	✓	✓

8738	\[ {} \frac {y^{\prime }}{x +y} = 0 \]	✓	✓	✓

8739	\[ {} \frac {y^{\prime }}{x} = 0 \]	✓	✓	✓

8740	\[ {} y^{\prime } = 0 \]	✓	✓	✓

8741	\[ {} y = x {y^{\prime }}^{2}+{y^{\prime }}^{2} \]	✓	✓	✓

8742	\[ {} y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}} \]	✓	✓	✓

8743	\[ {} 2 t +3 x+\left (x+2\right ) x^{\prime } = 0 \]	✓	✓	✓

8744	\[ {} y^{\prime } = \frac {1}{1-y} \]	✓	✓	✓

8745	\[ {} p^{\prime } = a p-b p^{2} \]	✓	✓	✓

8746	\[ {} y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0 \]	✓	✓	✓

8747	\[ {} x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}} \]	✓	✓	✗

8748	\[ {} x y^{\prime }-2 y+b y^{2} = c \,x^{4} \]	✓	✓	✗

8749	\[ {} x y^{\prime }-y+y^{2} = x^{{2}/{3}} \]	✓	✓	✗

8750	\[ {} u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}} \]	✓	✓	✗

8751	\[ {} y y^{\prime }-y = x \]	✓	✓	✗

8756	\[ {} y = x {y^{\prime }}^{2} \]	✓	✓	✓

8757	\[ {} y y^{\prime } = 1-x {y^{\prime }}^{3} \]	✓	✓	✗

8758	\[ {} f^{\prime } = \frac {1}{f} \]	✓	✓	✓

8770	\[ {} y^{\prime } = -4 \sin \left (x -y\right )-4 \]	✗	✓	✓

8771	\[ {} y^{\prime }+\sin \left (x -y\right ) = 0 \]	✓	✓	✓

8789	\[ {} x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \]	✓	✓	✗

8790	\[ {} \frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x \]	✓	✓	✓

8791	\[ {} \frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x \]	✓	✓	✗

8792	\[ {} y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \]	✓	✓	✓

8793	\[ {} y^{\prime } = x^{2}+y^{2} \]	✓	✓	✗

8794	\[ {} y^{\prime } = 2 \sqrt {y} \]	✓	✓	✓

8796	\[ {} y^{\prime } = \sqrt {1-y^{2}} \]	✓	✓	✓

8797	\[ {} y^{\prime } = x^{2}+y^{2}-1 \]	✓	✓	✗

8798	\[ {} y^{\prime } = 2 y \left (x \sqrt {y}-1\right ) \]	✓	✓	✗

8804	\[ {} y^{\prime }-y^{2}-x -x^{2} = 0 \]	✓	✓	✗

8860	\[ {} w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \]	✓	✓	✗

8886	\[ {} y^{\prime } = {\mathrm e}^{-\frac {y}{x}} \]	✓	✓	✓

8887	\[ {} y^{\prime } = 2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x} \]	✓	✓	✗

8889	\[ {} v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \]	✓	✓	✓

8921	\[ {} {y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4} \]	✗	✗	✗

8922	\[ {} \left (y-2 x y^{\prime }\right )^{2} = {y^{\prime }}^{3} \]	✓	✓	✗

8952	\[ {} y^{\prime } = y \left (1-y^{2}\right ) \]	✓	✓	✓

8976	\[ {} h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}} = b^{2} \]	✓	✓	✗

8980	\[ {} y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \]	✓	✓	✓

8982	\[ {} x^{2} y^{\prime }+{\mathrm e}^{-y} = 0 \]	✓	✓	✓

8984	\[ {} y^{\prime } = \frac {x y+3 x -2 y+6}{x y-3 x -2 y+6} \]	✗	✗	✗

8985	\[ {} y^{\prime } = 0 \]	✓	✓	✓

8986	\[ {} y^{\prime } = a \]	✓	✓	✓

8987	\[ {} y^{\prime } = x \]	✓	✓	✓

8988	\[ {} y^{\prime } = 1 \]	✓	✓	✓

8989	\[ {} y^{\prime } = a x \]	✓	✓	✓

8990	\[ {} y^{\prime } = a x y \]	✓	✓	✓

8991	\[ {} y^{\prime } = a x +y \]	✓	✓	✓

8992	\[ {} y^{\prime } = a x +b y \]	✓	✓	✓

8993	\[ {} y^{\prime } = y \]	✓	✓	✓

8994	\[ {} y^{\prime } = b y \]	✓	✓	✓

8995	\[ {} y^{\prime } = a x +b y^{2} \]	✓	✓	✗

8996	\[ {} c y^{\prime } = 0 \]	✓	✓	✓

8997	\[ {} c y^{\prime } = a \]	✓	✓	✓

8998	\[ {} c y^{\prime } = a x \]	✓	✓	✓

8999	\[ {} c y^{\prime } = a x +y \]	✓	✓	✓

9000	\[ {} c y^{\prime } = a x +b y \]	✓	✓	✓

9001	\[ {} c y^{\prime } = y \]	✓	✓	✓

9002	\[ {} c y^{\prime } = b y \]	✓	✓	✓

9003	\[ {} c y^{\prime } = a x +b y^{2} \]	✓	✓	✗

9004	\[ {} c y^{\prime } = \frac {a x +b y^{2}}{r} \]	✓	✓	✗

9005	\[ {} c y^{\prime } = \frac {a x +b y^{2}}{r x} \]	✓	✓	✗

9006	\[ {} c y^{\prime } = \frac {a x +b y^{2}}{r \,x^{2}} \]	✓	✓	✗

9007	\[ {} c y^{\prime } = \frac {a x +b y^{2}}{y} \]	✓	✓	✓

9008	\[ {} a \sin \left (x \right ) y x y^{\prime } = 0 \]	✓	✓	✓

9009	\[ {} f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi = 0 \]	✓	✓	✓

9010	\[ {} y^{\prime } = \sin \left (x \right )+y \]	✓	✓	✓

9011	\[ {} y^{\prime } = \sin \left (x \right )+y^{2} \]	✓	✓	✗

9012	\[ {} y^{\prime } = \cos \left (x \right )+\frac {y}{x} \]	✓	✓	✓

9013	\[ {} y^{\prime } = \cos \left (x \right )+\frac {y^{2}}{x} \]	✗	✗	✗

9014	\[ {} y^{\prime } = x +y+b y^{2} \]	✓	✓	✗

9015	\[ {} x y^{\prime } = 0 \]	✓	✓	✓

9016	\[ {} 5 y^{\prime } = 0 \]	✓	✓	✓

9017	\[ {} {\mathrm e} y^{\prime } = 0 \]	✓	✓	✓

9018	\[ {} \pi y^{\prime } = 0 \]	✓	✓	✓

9019	\[ {} \sin \left (x \right ) y^{\prime } = 0 \]	✓	✓	✓

9020	\[ {} f \left (x \right ) y^{\prime } = 0 \]	✓	✓	✓

9021	\[ {} x y^{\prime } = 1 \]	✓	✓	✓

9022	\[ {} x y^{\prime } = \sin \left (x \right ) \]	✓	✓	✓

9023	\[ {} \left (x -1\right ) y^{\prime } = 0 \]	✓	✓	✓

9024	\[ {} y y^{\prime } = 0 \]	✓	✓	✓

9025	\[ {} x y y^{\prime } = 0 \]	✓	✓	✓

9026	\[ {} x y \sin \left (x \right ) y^{\prime } = 0 \]	✓	✓	✓

9027	\[ {} \pi y \sin \left (x \right ) y^{\prime } = 0 \]	✓	✓	✓

9028	\[ {} x \sin \left (x \right ) y^{\prime } = 0 \]	✓	✓	✓

9029	\[ {} x \sin \left (x \right ) {y^{\prime }}^{2} = 0 \]	✓	✓	✓

9030	\[ {} y {y^{\prime }}^{2} = 0 \]	✓	✓	✓

9031	\[ {} {y^{\prime }}^{n} = 0 \]	✓	✓	✗

9032	\[ {} x {y^{\prime }}^{n} = 0 \]	✓	✓	✗

9033	\[ {} {y^{\prime }}^{2} = x \]	✓	✓	✓

9034	\[ {} {y^{\prime }}^{2} = x +y \]	✓	✓	✓

9035	\[ {} {y^{\prime }}^{2} = \frac {y}{x} \]	✓	✓	✓

9036	\[ {} {y^{\prime }}^{2} = \frac {y^{2}}{x} \]	✓	✓	✓

9037	\[ {} {y^{\prime }}^{2} = \frac {y^{3}}{x} \]	✓	✓	✓

4.1.42 Problems 4101 to 4200