12.10.27 problem 27

Internal problem ID [1831]
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 : 27
Date solved : Monday, January 27, 2025 at 05:36:42 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y&=x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(x^2+6)*y(x)=x^4,y(x), singsol=all)
 

\[ y = x^{2} \left (1+c_2 \sin \left (x \right )+\cos \left (x \right ) c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 38

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+(x^2+6)*y[x]==x^4,y[x],x,IncludeSingularSolutions -> True]
 

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