7.4.25 problem 25

Internal problem ID [97]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 25
Date solved : Friday, February 07, 2025 at 07:49:18 AM
CAS classification : [_linear]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 y x^{3}&=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: 0.028 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.099 (sec). Leaf size: 28

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

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