Internal problem ID [13231]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.3 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+8 y={\mathrm e}^{4 x}} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{2 x} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)-6*diff(y(x),x)+8*y(x)=exp(4*x),exp(2*x)],y(x), singsol=all)
\[ y = \left (\frac {{\mathrm e}^{2 x} \left (2 x +2 c_{1} -1\right )}{4}+c_{2} \right ) {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 31
DSolve[y''[x]-6*y'[x]+8*y[x]==Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{2 x}+e^{4 x} \left (\frac {x}{2}-\frac {1}{4}+c_2\right ) \]