Differential Equation

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #61

Solve: `x\dy-y\dx=\sqrt{x^2+y^2}dx`
Ans: `tan^{-1}(y/x) = x+c`
SEE SOLUTION

Question No: #62

Solve: `(x-\sqrt{xy})dy=y\ dx`

Question No: #63

Solve: `(x^2+y^2)dx-2xy\ dy=0` given `y=0` when `x=1`
Ans: `y^2/x = x - 1`
SEE SOLUTION

Question No: #64

Solve: `x^2(y-1)dx+y^2(x-1)dy=0`

Question No: #65

Solve: `(x^2y^2+xy)ydx+(x^2y^2-1)xdy=0`
Ans: `xy-\log|y|=c`
SEE SOLUTION

Question No: #66

Solve: `(4x^2y-6)dx+x^3dy=0`
Ans: `xy + \frac{3}{2x} = c`
SEE SOLUTION

Question No: #67

Solve: `(3xy+y^2)dx+(x^2+xy)dy=0`

Question No: #68

Solve: `(xy^2+x)dx+(x^2y+y)dy=0` when `x=0`, `y=1`
Ans: `x^2y^2 + x^2 + y^2 = 1`
SEE SOLUTION

Question No: #69

Solve: `(x^2-yx^2)dy+(y^2+x^2y^2)dx=0`
Ans: `log |y| +1/y + 1/x = x + c`
SEE SOLUTION

Question No: #70

Solve: `(x^2+xy)dy=(x^2+y^2)dx`