73.16.12 problem 24.1 (L)

Internal problem ID [15524]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (L)
Date solved : Tuesday, January 28, 2025 at 08:01:06 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=x^{3} {\mathrm e}^{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 26

dsolve(x*diff(y(x),x$2)-diff(y(x),x)-4*x^3*y(x)=x^3*exp(x^2),y(x), singsol=all)
 

\[ y = \sinh \left (x^{2}\right ) c_{2} +\cosh \left (x^{2}\right ) c_{1} +\frac {{\mathrm e}^{x^{2}} x^{2}}{8} \]

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 47

DSolve[x*D[y[x],{x,2}]-D[y[x],x]-4*x^3*y[x]==x^3*Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{16} \left (\left (2 x^2-1+16 c_1\right ) \cosh \left (x^2\right )+\sinh \left (x^2\right ) \left (\log \left (e^{2 x^2}\right )-1+16 i c_2\right )\right ) \]