12.10.18 problem 18

Internal problem ID [1822]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number : 18
Date solved : Monday, January 27, 2025 at 05:36:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=8 x^{5} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

dsolve(x*diff(y(x),x$2)-diff(y(x),x)-4*x^3*y(x)=8*x^5,y(x), singsol=all)
 

\[ y = \sinh \left (x^{2}\right ) c_2 +\cosh \left (x^{2}\right ) c_1 -2 x^{2} \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 28

DSolve[x*D[y[x],{x,2}]-D[y[x],x]-4*x^3*y[x]==8*x^5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 x^2+c_1 \cosh \left (x^2\right )+i c_2 \sinh \left (x^2\right ) \]