Internal problem ID [10316]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60.
Exact equation. Integrating factor. Page 139
Problem number: Ex 8.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$3)-5*x*diff(y(x),x$2)+(4*x^4+5)*diff(y(x),x)-8*x^3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{1}+c_{2} \cos \left (x^{2}\right )+c_{3} \sin \left (x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.249 (sec). Leaf size: 44
DSolve[x^2*y'''[x]-5*x*y''[x]+(4*x^4+5)*y'[x]-8*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x^2+\frac {1}{2} i c_2 e^{-i x^2}-\frac {1}{8} c_3 e^{i x^2} \\ \end{align*}