Internal problem ID [5316]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary
problems. Page 39
Problem number: 22 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x y^{\prime }-2 y=x^{3} {\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve([x*diff(y(x),x)=2*y(x)+x^3*exp(x),y(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\left (-{\mathrm e}^{x}+{\mathrm e}\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 16
DSolve[{x*y'[x]==2*y[x]+x^3*Exp[x],{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (e^x-e\right ) x^2 \]