Internal problem ID [2314]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.9, Reduction of Order. page
572
Problem number: Problem 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {4 x^{2} y^{\prime \prime }+y-\sqrt {x}\, \ln \left (x \right )=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \sqrt {x} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve([4*x^2*diff(y(x),x$2)+y(x)=sqrt(x)*ln(x),sqrt(x)],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {x}\, c_{2} +\sqrt {x}\, \ln \left (x \right ) c_{1} +\frac {\ln \left (x \right )^{3} \sqrt {x}}{24} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 29
DSolve[4*x^2*y''[x]+y[x]==Sqrt[x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} \sqrt {x} \left (\log ^3(x)+12 c_2 \log (x)+24 c_1\right ) \\ \end{align*}