Internal problem ID [12137]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 59.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y=a \,x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve((x-x^2)*diff(y(x),x)+(2*x^2-1)*y(x)-a*x^3=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (-a \left ({\mathrm e}^{-2} \operatorname {Ei}_{1}\left (2 x -2\right )+\frac {2 \,{\mathrm e}^{-2 x}}{-2 x +2}\right )+c_{1} \right ) \left ({\mathrm e}^{2 x} x^{2}-{\mathrm e}^{2 x} x \right ) \]
✓ Solution by Mathematica
Time used: 0.473 (sec). Leaf size: 39
DSolve[(x-x^2)*y'[x]+(2*x^2-1)*y[x]-a*x^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (a e^{2 x-2} (x-1) \operatorname {ExpIntegralEi}(2-2 x)+a-c_1 e^{2 x} (x-1)\right ) \]