Internal problem ID [4353]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page
435
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{x} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([3*x*diff(y(x),x$2)-2*(3*x-1)*diff(y(x),x)+(3*x-2)*y(x)=0,exp(x)],y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} x^{\frac {1}{3}} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 21
DSolve[3*x*y''[x]-2*(3*x-1)*y'[x]+(3*x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (3 c_2 \sqrt [3]{x}+c_1\right ) \\ \end{align*}