12.2.18 problem 18

Internal problem ID [1554]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 18
Date solved : Monday, January 27, 2025 at 04:59:53 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+\left (2 x^{2}+1\right ) y&=x^{3} {\mathrm e}^{-x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

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

\[ y = \frac {\left (x^{4}+4 c_1 \right ) {\mathrm e}^{-x^{2}}}{4 x} \]

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 27

DSolve[x*D[y[x],x] +(1+2*x^2)*y[x]==x^3*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-x^2} \left (x^4+4 c_1\right )}{4 x} \]