Differential Equations
Exact/Integrable Equations
MMTS_Full_Test_20
Grade 12
Question:
The solution of the differential equation $(1-xy-x^5y^5)dx-x^2(x^4y^4+1)dy=0$ given by ($c$ is arbitrary constant)
$x=ce^{xy+\frac{1}{5}x^5y^5}$
$x=ce^{xy-\frac{1}{5}x^2y^5}$
$x=ce^{x^2y^2+\frac{1}{5}x^5y^5}$
$x=ce^{x^2y^2-\frac{1}{5}x^5y^5}$
Step-by-Step Solution
Key Concept: Rearrange to exact form; identify integrating factor
Rearranging: $dx/x^2 - y\,dx/x - x^4y^5\,dx - x^4y^4\,dy=0$. Integrating gives $x=ce^{xy+x^5y^5/5}$.
Correct Answer: 1