20.2 problem section 9.4, problem 8

Internal problem ID [1573]

Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of Parameters for Higher Order Equations. Page 503
Problem number: section 9.4, problem 8.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 y^{\prime } x +2 y-30 x^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 32

dsolve(4*x^3*diff(y(x),x$3)+4*x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+2*y(x)=30*x^2,y(x), singsol=all)
 

\[ y \relax (x ) = 2 \ln \relax (x ) x^{2}-\frac {32 x^{2}}{15}+x^{2} c_{1}+\frac {c_{2}}{\sqrt {x}}+c_{3} \sqrt {x} \]

Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 38

DSolve[4*x^3*y'''[x]+4*x^2*y''[x]-5*x*y'[x]+2*y[x]==30*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2 x^2 \log (x)+\frac {\left (-\frac {32}{15}+c_3\right ) x^{5/2}+c_2 x+c_1}{\sqrt {x}} \\ \end{align*}