Maths · The solution of differential equation by the method of separation of variables
d x=x^{2} d y \)
\( \left(1-x y+x^{2} y^{2}\right) d x=x^{2} d y \)
- A. \( _{y}=\frac{1}{x} \tan (\ln |c y|) \)
- B. \( _{x}=\frac{1}{y} \tan (\ln |c x|) \)
- C. \( x=\frac{1}{y} \cot (\ln |c y|) \)
- D. \( y=\frac{1}{x} \cot (\ln |c x|) \)
Step-by-step solution
Rewrite the differential equation as x d(xy) = (1 + (xy)^2) dx, then separate variables: d(xy)/(1+(xy)^2) = dx/x. Integrate to get arctan(xy) = ln|x| + C, so xy = tan(ln|x|+C). Write C = ln|c| to obtain xy = tan(ln|c x|), which is equivalent to x = (1/y) tan(ln|c x|).
Related MCQs
- Assertion A normal is drawn at a point \) of curve. It meets the -axis and the -axis in point and , respectively, such that where is the ori…
- A certain radioactive material is known to decay at a rate proportional to the amount present. If after one hour it is observed that 10 perc…
- The normal at any point \) of curve meets the -axis at and is the foot of the ordinate at If }{1+x^{2}}, \) then equation of such curve, giv…
- Solution of the differential equation is…