83.14.6 problem 6

Internal problem ID [19185]
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 (F) at page 42
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 01:11:47 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+y(x)=sin(3*x)-cos(1/2*x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]+y[x]==Sin[3*x]-Cos[1/2*x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} (-\sin (3 x)+(-2+8 c_1) \cos (x)-2 (x+1-4 c_2) \sin (x)-4) \]