12.10.21 problem 21

Internal problem ID [1825]
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 : 21
Date solved : Monday, January 27, 2025 at 05:36:29 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y&=x^{{7}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 21

dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2+3)*y(x)=x^(7/2),y(x), singsol=all)
 

\[ y = \frac {\sqrt {x}\, \left (4 c_2 \sin \left (x \right )+4 \cos \left (x \right ) c_1 +x \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 48

DSolve[4*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+(4*x^2+3)*y[x]==x^(7/2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-i x} \sqrt {x} \left (e^{i x} x-2 i c_2 e^{2 i x}+4 c_1\right ) \]