Internal problem ID [673]
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: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime }+4 x^{3} y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= \sin \left (x^{2}\right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([x*diff(y(x),x$2)-diff(y(x),x)+4*x^3*y(x)=0,sin(x^2)],y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (x^{2}\right )+c_{2} \cos \left (x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 20
DSolve[x*y''[x]-y'[x]+4*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos \left (x^2\right )+c_2 \sin \left (x^2\right ) \\ \end{align*}