2.1302   ODE No. 1302

\[ \text {A0} y(x) (a x+b)+\text {A1} (a x+b) y'(x)+\text {A2} (a x+b)^2 y''(x)=0 \]

✓ Mathematica : cpu = 0.0472563 (sec), leaf count = 243

DSolve[A0*(b + a*x)*y[x] + A1*(b + a*x)*Derivative[1][y][x] + A2*(b + a*x)^2*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \left (\frac {2 b}{a}+2 x\right )^{\frac {\text {A1}}{2 a \text {A2}}} (2 a \text {A2} x+2 \text {A2} b)^{-\frac {\text {A1}}{2 a \text {A2}}} \left (-\frac {\text {A0} \left (\frac {b}{a}+x\right )}{a \text {A2}}\right )^{\frac {1}{2}-\frac {\text {A1}}{2 a \text {A2}}} I_{\frac {\text {A1}}{a \text {A2}}-1}\left (2 \sqrt {-\frac {\text {A0} \left (\frac {b}{a}+x\right )}{a \text {A2}}}\right )+c_2 (-1)^{1-\frac {\text {A1}}{a \text {A2}}} \left (\frac {2 b}{a}+2 x\right )^{\frac {\text {A1}}{2 a \text {A2}}} (2 a \text {A2} x+2 \text {A2} b)^{-\frac {\text {A1}}{2 a \text {A2}}} \left (-\frac {\text {A0} \left (\frac {b}{a}+x\right )}{a \text {A2}}\right )^{\frac {1}{2}-\frac {\text {A1}}{2 a \text {A2}}} K_{\frac {\text {A1}}{a \text {A2}}-1}\left (2 \sqrt {-\frac {\text {A0} \left (\frac {b}{a}+x\right )}{a \text {A2}}}\right )\right \}\right \}\]

✓ Maple : cpu = 0.1 (sec), leaf count = 98

dsolve(A2*(a*x+b)^2*diff(diff(y(x),x),x)+A1*(a*x+b)*diff(y(x),x)+A0*(a*x+b)*y(x)=0,y(x))
 

\[y \left (x \right ) = \left (a x +b \right )^{-\frac {-a \operatorname {A2} +\operatorname {A1}}{2 a \operatorname {A2}}} \left (\operatorname {BesselY}\left (\frac {a \operatorname {A2} -\operatorname {A1}}{a \operatorname {A2}}, 2 \sqrt {\operatorname {A0}}\, \sqrt {\frac {a x +b}{a^{2} \operatorname {A2}}}\right ) c_{2} +\operatorname {BesselJ}\left (\frac {a \operatorname {A2} -\operatorname {A1}}{a \operatorname {A2}}, 2 \sqrt {\operatorname {A0}}\, \sqrt {\frac {a x +b}{a^{2} \operatorname {A2}}}\right ) c_{1} \right )\]