12.10.20 problem 20

Internal problem ID [1824]
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 : 20
Date solved : Monday, January 27, 2025 at 05:36:27 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=8 x^{{5}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 22

dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(3-16*x^2)*y(x)=8*x^(5/2),y(x), singsol=all)
 

\[ y = \sqrt {x}\, \left (-\frac {1}{2}+\sinh \left (2 x \right ) c_2 +\cosh \left (2 x \right ) c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 39

DSolve[4*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+(3-16*x^2)*y[x]==8*x^(5/2),y[x],x,IncludeSingularSolutions -> True]
 

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