Internal problem ID [1138]
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: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{2 x} \end {align*}
With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 18
dsolve([(3*x-1)*diff(diff(y(x),x),x)-(3*x+2)*diff(y(x),x)-(6*x-8)*y(x) = 0, exp(2*x), y(0) = 2, D(y)(0) = 3], singsol=all)
\[ y \left (x \right ) = 2 \,{\mathrm e}^{2 x}-x \,{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 21
DSolve[(3*x-1)*y''[x]-(3*x+2)*y'[x]-(6*x-8)*y[x]==0,{y[0]==2,y'[0]==3},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 e^{2 x}-e^{-x} x \]