83.44.8 problem Ex 8 page 40

Internal problem ID [19536]
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 8 page 40
Date solved : Tuesday, January 28, 2025 at 01:50:03 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 48

dsolve(diff(y(x),x$3)+a^2*diff(y(x),x)=sin(a*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 46

DSolve[D[y[x],{x,3}]+a^2*D[y[x],x]==Sin[a*x],y[x],x,IncludeSingularSolutions -> True]
 

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