12.10.24 problem 24

Internal problem ID [1828]
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 : 24
Date solved : Monday, January 27, 2025 at 05:36:37 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=x^{{3}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

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

\[ y = \frac {15 x^{4} c_2 -4 x^{{5}/{2}}+15 c_1}{15 x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 27

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

\[ y(x)\to -\frac {4 x^{3/2}}{15}+c_2 x^3+\frac {c_1}{x} \]