12.10.11 problem 11

Internal problem ID [1815]
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 : 11
Date solved : Monday, January 27, 2025 at 05:35:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{{5}/{2}} \end{align*}

✓ Solution by Maple

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

dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=x^(5/2),y(x), singsol=all)
 

\[ y = c_2 \,x^{3}+c_1 \,x^{2}-4 x^{{5}/{2}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 23

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==x^(5/2),y[x],x,IncludeSingularSolutions -> True]
 

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