83.49.16 problem Ex 16 page 132

Internal problem ID [19629]
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 VIII. Linear equations of second order
Problem number : Ex 16 page 132
Date solved : Tuesday, January 28, 2025 at 02:05:22 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=8 x^{3} \sin \left (x^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(x*diff(y(x),x$2)-diff(y(x),x)-4*x^3*y(x)=8*x^3*sin(x^2),y(x), singsol=all)
 

\[ y \left (x \right ) = \sinh \left (x^{2}\right ) c_{2} +\cosh \left (x^{2}\right ) c_{1} -\sin \left (x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 29

DSolve[x*D[y[x],{x,2}]-D[y[x],x]-4*x^3*y[x]==8*x^3*Sin[x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sin \left (x^2\right )+c_1 \cosh \left (x^2\right )+i c_2 \sinh \left (x^2\right ) \]