Internal problem ID [255]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 60.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y-8 x^{\frac {4}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+3*y(x)=8*x^(4/3),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sqrt {x}+x^{\frac {3}{2}} c_{1}-\frac {72 x^{\frac {4}{3}}}{5} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 31
DSolve[4*x^2*y''[x]-4*x*y'[x]+3*y[x]==8*x^(4/3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} \sqrt {x} \left (-72 x^{5/6}+5 c_2 x+5 c_1\right ) \\ \end{align*}