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]]
\[ \boxed {4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 y^{\prime } x +2 y=30 x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {\left (c_{1} +2 \ln \left (x \right )-\frac {32}{15}\right ) x^{\frac {5}{2}}+c_{3} x +c_{2}}{\sqrt {x}} \]
✓ 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]
\[ y(x)\to 2 x^2 \log (x)+\frac {\left (-\frac {32}{15}+c_3\right ) x^{5/2}+c_2 x+c_1}{\sqrt {x}} \]