Question

11 poro The rght hand side of the following trst order proclen We abtain the tol lowing separable equation in tha variables r and v Sohing ths equation an implic gareral soution in teems of z, r can be witen in the fore Tra sfoming back to the variables r and y the ebove equarion becomes Nent using the initiel condition y/0) 0indC

Answer 1

"Let v = 3 x - 7 y + 1 differentiating w r t x both x both sides dv/dx = 3 - 7 dy/dx + 7 dy/dx = 3 - dv/dx dy/dx = 1/7 (3 - dv/dx) Now, putting this value in (1) 1/7 (3 - dv/dx) = (v)^1/2 + 3/7 (3 - dv/dx) = 7 v^1/2 + 3 3 - dv/dx = 7^1/2 + 3 dv/dx = -7 v^1/2 so, v"" = -7 v^1/2 Ans b) solving this differential equation dv/dx = -7 v^1/2 dv/v^1/2 = -dx Integrating both sides, we get integral dv/ v^1/2 = -7 integral dx = v^- 1/2 + 1/ - 1 /2 + 1 = -7 x + c
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