12.20.2 problem section 9.4, problem 8

Internal problem ID [2223]
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
Date solved : Monday, January 27, 2025 at 05:43:46 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y&=30 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 24

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)
 

\[ y = \frac {\left (c_1 +2 \ln \left (x \right )-\frac {32}{15}\right ) x^{{5}/{2}}+x c_3 +c_2}{\sqrt {x}} \]

✓ Solution by Mathematica

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

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

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