23.3.22 problem 9(c)

Internal problem ID [4163]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 9(c)
Date solved : Monday, January 27, 2025 at 08:41:07 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 25 y^{\prime \prime }-30 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 15

dsolve([25*diff(y(x),x$2)-30*diff(y(x),x)+9*y(x)=0,y(1) = 0, D(y)(1) = 2],y(x), singsol=all)
 

\[ y \left (x \right ) = 2 \,{\mathrm e}^{-\frac {3}{5}+\frac {3 x}{5}} \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 19

DSolve[{25*D[y[x],{x,2}]-30*D[y[x],x]+9*y[x]==0,{y[1]==0,Derivative[1][y][1] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^{\frac {3 (x-1)}{5}} (x-1) \]