64.10.30 problem 30

Internal problem ID [13436]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 05:42:27 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=9 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 14

dsolve([4*diff(y(x),x$2)-12*diff(y(x),x)+9*y(x)=0,y(0) = 4, D(y)(0) = 9],y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {3 x}{2}} \left (3 x +4\right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

DSolve[{4*D[y[x],{x,2}]-12*D[y[x],x]+9*y[x]==0,{y[0]==4,Derivative[1][y][0] ==9}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x/2} (3 x+4) \]