Internal problem ID [1108]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page
253
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -y=\frac {4}{x^{2}}} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=4/x^2,x],y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x +\frac {c_{1}}{x}+\frac {4}{3 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 23
DSolve[x^2*y''[x]+x*y'[x]-y[x]==4/x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4}{3 x^2}+\frac {c_1}{x}+c_2 x \]