83.17.10 problem 10

Internal problem ID [19206]
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. Misc. Examples on chapter III at page 50
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 01:13:25 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 36

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

\[ y \left (x \right ) = \frac {\left (\sin \left (x \right )-4\right ) \cos \left (x \right )^{2}}{4}+\frac {\left (4 c_{1} -3 x \right ) \cos \left (x \right )}{4}+2+\frac {\left (4 c_{2} +2\right ) \sin \left (x \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.151 (sec). Leaf size: 43

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

\[ y(x)\to \frac {1}{16} (2 \sin (x)+\sin (3 x)-8 \cos (2 x)-4 (3 x-4 c_1) \cos (x)+16 c_2 \sin (x)+24) \]