40.4.19 problem 22 (a)

Internal problem ID [6659]
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)
Date solved : Monday, January 27, 2025 at 02:18:19 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=2 y+x^{3} {\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

dsolve([x*diff(y(x),x)=2*y(x)+x^3*exp(x),y(1) = 0],y(x), singsol=all)
 

\[ y = -\left ({\mathrm e}-{\mathrm e}^{x}\right ) x^{2} \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 16

DSolve[{x*D[y[x],x]==2*y[x]+x^3*Exp[x],{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (e^x-e\right ) x^2 \]