8.4.25 problem 25

Internal problem ID [728]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 25
Date solved : Monday, January 27, 2025 at 02:59:22 AM
CAS classification : [_linear]

\begin{align*} 3 x^{3} y+\left (x^{2}+1\right ) y^{\prime }&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 34

dsolve([3*x^3*y(x)+(x^2+1)*diff(y(x),x) = 6*x/exp(3/2*x^2),y(0) = 1],y(x), singsol=all)
 

\[ y = \left (3 x^{2} \sqrt {x^{2}+1}+3 \sqrt {x^{2}+1}-2\right ) {\mathrm e}^{-\frac {3 x^{2}}{2}} \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 28

DSolve[{3*x^3*y[x]+(x^2+1)*D[y[x],x] == 6*x/Exp[3/2*x^2],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {3 x^2}{2}} \left (3 \left (x^2+1\right )^{3/2}-2\right ) \]