Internal problem ID [78]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {3 x^{3} y+\left (x^{2}+1\right ) y^{\prime }-6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
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)
\[ y \relax (x ) = \left (3 x^{2} \sqrt {x^{2}+1}+3 \sqrt {x^{2}+1}-2\right ) {\mathrm e}^{-\frac {3 x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 28
DSolve[{3*x^3*y[x]+(x^2+1)*y'[x] == 6*x/Exp[3/2*x^2],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\frac {3 x^2}{2}} \left (3 \left (x^2+1\right )^{3/2}-2\right ) \\ \end{align*}