Internal problem ID [13254]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 15. General solutions to Homogeneous linear differential equations. Additional
exercises page 294
Problem number: 15.6 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }-3 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([diff(y(x),x$2)+2*diff(y(x),x)-3*y(x)=0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y = \frac {\left ({\mathrm e}^{4 x}-1\right ) {\mathrm e}^{-3 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 21
DSolve[{y''[x]+2*y'[x]-3*y[x]==0,{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-3 x} \left (e^{4 x}-1\right ) \]