Internal problem ID [12494]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 122.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }-y^{\prime }=x^{2} {\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 17
dsolve([x*diff(y(x),x$2)-diff(y(x),x)=x^2*exp(x),y(0) = -1, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \left (-1+x \right ) {\mathrm e}^{x}+\frac {c_{1} x^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 22
DSolve[{x*y''[x]-y'[x]==x^2*Exp[x],{y[0]==-1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (x-1)+\frac {c_1 x^2}{2} \]