83.48.6 problem Ex 6 page 100

Internal problem ID [19598]
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 VII. Exact differential equations.
Problem number : Ex 6 page 100
Date solved : Tuesday, January 28, 2025 at 08:32:57 PM
CAS classification : [[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 32

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

\[ y \left (x \right ) = -\arcsin \left (\frac {2 c_{2} x^{{3}/{2}}+\left (3 \ln \left (x \right )-3\right ) \sqrt {x}-2 c_{1}}{3 \sqrt {x}}\right ) \]

✓ Solution by Mathematica

Time used: 57.887 (sec). Leaf size: 59

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

\begin{align*} y(x)\to \arcsin \left (-\log (x)+\frac {2 c_1}{3 \sqrt {x}}+\frac {c_2 x}{2}+1\right ) \\ y(x)\to \arcsin \left (-\log (x)+\frac {2 c_1}{3 \sqrt {x}}+\frac {c_2 x}{2}+1\right ) \\ \end{align*}