Internal problem ID [1141]
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: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {\left (x^{2}-4\right ) y^{\prime \prime }+4 y^{\prime } x +2 y=2+x} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {1}{-2+x} \end {align*}
With initial conditions \begin {align*} \left [y \left (0\right ) = -{\frac {1}{3}}, y^{\prime }\left (0\right ) = -1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve([(x^2-4)*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*y(x) = 2+x, 1/(-2+x), y(0) = -1/3, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{3}+6 x^{2}+24 x +8}{6 x^{2}-24} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 30
DSolve[(x^2-4)*y''[x]+4*x*y'[x]+2*y[x]==x+2,{y[1]==5/4,y'[1]==3/2},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-2 x^3-12 x^2+54 x+5}{48-12 x^2} \]