Internal problem ID [11606]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises
page 37
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
\[ \boxed {3 x^{2} y^{2}-y^{3}+\left (2 y x^{3}-3 y^{2} x +1\right ) y^{\prime }=-2 x} \] With initial conditions \begin {align*} [y \left (-2\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 28.797 (sec). Leaf size: 210
dsolve([(3*x^2*y(x)^2-y(x)^3+2*x)+(2*x^3*y(x)-3*x*y(x)^2+1)*diff(y(x),x)=0,y(-2) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\frac {2^{\frac {2}{3}} \left (1+i \sqrt {3}\right ) {\left (\left (2 x^{7}+3 \sqrt {3}\, \sqrt {\frac {4 x^{10}+4 x^{8}+44 x^{5}+72 x^{3}+27 x -4}{x}}+36 x^{2}+27\right ) x^{2}\right )}^{\frac {2}{3}}}{2}+x \left (2 x^{2} {\left (\left (2 x^{7}+3 \sqrt {3}\, \sqrt {\frac {4 x^{10}+4 x^{8}+44 x^{5}+72 x^{3}+27 x -4}{x}}+36 x^{2}+27\right ) x^{2}\right )}^{\frac {1}{3}}+\left (x^{5}+3\right ) 2^{\frac {1}{3}} \left (i \sqrt {3}-1\right )\right )}{6 {\left (\left (2 x^{7}+3 \sqrt {3}\, \sqrt {\frac {4 x^{10}+4 x^{8}+44 x^{5}+72 x^{3}+27 x -4}{x}}+36 x^{2}+27\right ) x^{2}\right )}^{\frac {1}{3}} x} \]
✓ Solution by Mathematica
Time used: 60.368 (sec). Leaf size: 250
DSolve[{(3*x^2*y[x]^2-y[x]^3+2*x)+(2*x^3*y[x]-3*x*y[x]^2+1)*y'[x]==0,{y[-2]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 \sqrt [3]{2} \left (1-i \sqrt {3}\right ) x^6+4 \sqrt [3]{-2 x^9-36 x^4-27 x^2+3 \sqrt {3} \sqrt {x^3 \left (4 x^{10}+4 x^8+44 x^5+72 x^3+27 x-4\right )}} x^3+\left (1+i \sqrt {3}\right ) \left (-4 x^9-72 x^4-54 x^2+6 \sqrt {3} \sqrt {x^3 \left (4 x^{10}+4 x^8+44 x^5+72 x^3+27 x-4\right )}\right )^{2/3}+6 \sqrt [3]{2} \left (1-i \sqrt {3}\right ) x}{12 x \sqrt [3]{-2 x^9-36 x^4-27 x^2+3 \sqrt {3} \sqrt {x^3 \left (4 x^{10}+4 x^8+44 x^5+72 x^3+27 x-4\right )}}} \]