83.44.6 problem Ex 6 page 38

Internal problem ID [19534]
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 6 page 38
Date solved : Tuesday, January 28, 2025 at 01:50:00 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 49

dsolve(diff(y(x),x$3)+y(x)=(1+exp(x))^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{1} +{\mathrm e}^{x}+{\mathrm e}^{2 x}+\frac {{\mathrm e}^{3 x}}{9}\right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.541 (sec). Leaf size: 78

DSolve[D[y[x],{x,3}]+y[x]==(1+Exp[x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-x}}{9}+e^x+\frac {e^{2 x}}{9}+c_1 e^{-x}+c_3 e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+1 \]