Internal problem ID [8722]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1142.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {5 \left (a x +b \right ) y^{\prime \prime }+8 a y^{\prime }+c \left (a x +b \right )^{\frac {1}{5}} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.041 (sec). Leaf size: 59
dsolve(5*(a*x+b)*diff(diff(y(x),x),x)+8*a*diff(y(x),x)+c*(a*x+b)^(1/5)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sinh \left (\frac {\left (a x +b \right )^{\frac {3}{5}} \sqrt {-5 c}}{3 a}\right )}{\left (a x +b \right )^{\frac {3}{5}}}+\frac {c_{2} \cosh \left (\frac {\left (a x +b \right )^{\frac {3}{5}} \sqrt {-5 c}}{3 a}\right )}{\left (a x +b \right )^{\frac {3}{5}}} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 89
DSolve[c*(b + a*x)^(1/5)*y[x] + 8*a*y'[x] + 5*(b + a*x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 a \left (2 c_1 \cos \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )+c_2 \sin \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )\right )}{\sqrt {5} \sqrt {c} (a x+b)^{3/5}} \\ \end{align*}