12.10.22 problem 22

Internal problem ID [1826]
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 : 22
Date solved : Monday, January 27, 2025 at 05:36:33 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y&=3 x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 20

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

\[ y = x \sinh \left (x \right ) c_2 +x \cosh \left (x \right ) c_1 -3 x^{2} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 29

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

\[ y(x)\to \frac {1}{2} x \left (-6 x+2 c_1 e^{-x}+c_2 e^x\right ) \]