83.16.7 problem 7

Internal problem ID [19196]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (H) at page 47
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 01:13:02 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\left (x -1\right ) {\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)+4*diff(y(x),x)-12*y(x)=(x-1)*exp(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (\left (x^{2}-\frac {9}{4} x +16 c_{2} \right ) {\mathrm e}^{8 x}+16 c_{1} \right ) {\mathrm e}^{-6 x}}{16} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}]+4*D[y[x],x]-12*y[x]==(x-1)*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\frac {x^2}{16}-\frac {9 x}{64}+\frac {9}{512}+c_2\right )+c_1 e^{-6 x} \]