10.7.23 problem 25

Internal problem ID [1271]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 25
Date solved : Monday, January 27, 2025 at 04:49:16 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-\beta \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 28

dsolve([2*diff(y(x),x$2) +3*diff(y(x),x)-2*y(x) = 0,y(0) = 1, D(y)(0) = -beta],y(x), singsol=all)
 

\[ y = -\frac {\left (2 \,{\mathrm e}^{\frac {5 x}{2}} \beta -4 \,{\mathrm e}^{\frac {5 x}{2}}-2 \beta -1\right ) {\mathrm e}^{-2 x}}{5} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 67

DSolve[{D[y[x],{x,2}]+3*D[y[x],x]-2*y[x]==0,{y[0]==1,Derivative[1][y][0] ==-\[Beta]}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{34} e^{-\frac {1}{2} \left (3+\sqrt {17}\right ) x} \left (2 \sqrt {17} \beta +\left (-2 \sqrt {17} \beta +3 \sqrt {17}+17\right ) e^{\sqrt {17} x}-3 \sqrt {17}+17\right ) \]