60.3.138 problem 1142

Internal problem ID [11148]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1142
Date solved : Tuesday, January 28, 2025 at 05:41:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 5 \left (a x +b \right ) y^{\prime \prime }+8 a y^{\prime }+c \left (a x +b \right )^{{1}/{5}} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.463 (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)
 

\[ y = \frac {c_{1} \sinh \left (\frac {\left (a x +b \right )^{{3}/{5}} \sqrt {5}\, \sqrt {-c}}{3 a}\right )+c_{2} \cosh \left (\frac {\left (a x +b \right )^{{3}/{5}} \sqrt {5}\, \sqrt {-c}}{3 a}\right )}{\left (a x +b \right )^{{3}/{5}}} \]

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 89

DSolve[c*(b + a*x)^(1/5)*y[x] + 8*a*D[y[x],x] + 5*(b + a*x)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 a \left (2 c_1 \cos \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )+c_2 \sin \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )\right )}{\sqrt {5} \sqrt {c} (a x+b)^{3/5}} \]