Integral Calculas
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The document discusses solving a first order, first degree homogeneous differential equation. 1) The given equation is dy/dx = (x^2 - y^2)/xy, which is homogeneous in x and y. 2) Putting y = vx transforms the equation into a separable equation in v and x. 3) Integrating both sides and applying logarithm rules yields the general solution as log(x^4) - log(1 - 2v^2) = constant.
Integral Calculas
- 3. SOLUTION OF LINEAR EQUATION Solution = y(I.F.)= . . +
- 5. EQUATION OF THE FIRST ORDER AND FIRST DEGREE
- 7. Given equation is = 22 ヰ も Put y = vx, then = + Therefore (1) becomes v +x = 1 2 x = 12 - v = 122 Separating the variables. 122 = Integrating both sides, 1 ｐ 122 = 1 1 4 1 4 1 22 = 1 + Or - 1 4 1 22 = + 4logx +log(1 - 22) = 4 Or log 4 1 22 = 4 4 1 22 2 = 3 =
- 8. THANK YOU -GUIDED BY NAVEEN SIR