Internal problem ID [675]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page
172
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x^{\frac {1}{4}} {\mathrm e}^{2 \sqrt {x}} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve([x^2*diff(y(x),x$2)-(x-1875/10000)*y(x)=0,x^(1/4)*exp(2*sqrt(x))],y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {1}{4}} \sinh \left (2 \sqrt {x}\right )+c_{2} x^{\frac {1}{4}} \cosh \left (2 \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 41
DSolve[x^2*y''[x]-(x-1875/10000)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-2 \sqrt {x}} \sqrt [4]{x} \left (2 c_1 e^{4 \sqrt {x}}-c_2\right ) \\ \end{align*}