83.44.13 problem Ex 13 page 47

Internal problem ID [19541]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter III. Ordinary linear differential equations with constant coefficients
Problem number : Ex 13 page 47
Date solved : Tuesday, January 28, 2025 at 01:50:09 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=2 \sinh \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=2*sinh(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==2*Sinh[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{16} e^{-2 x} \left (-8 x^2+e^{4 x}+16 c_2 x+16 c_1\right ) \]