What is a solution to the differential equation #sqrtx+sqrtydy/dx# with y(1)=4?

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Answer 1 · 2016-07-25T19:02:10

#x^(3/2)+y^(3/2)=9#.

Rewriting the Diff. Eqn. as, #sqrtxdx+sqrtydy=0#, we notice that it is a Separable Variable type Diff. Eqn.

To find its General Soln. , we integrate term-wise , i.e.,

#intsqrtxdx+intsqrtydy=C#

#:. x^(3/2)/(3/2)+y^(3/2)/(3/2)=C#. or,

#x^(3/2)+y^(3/2)=3/2*C.......(1)#

To determine #C#, we use the given cond. - called The Initial Cond. - that #y(1)=4#, meaning, when #x=1, y=4#.

Sub.ing in #(1)#, we get, #1+4^(3/2)=3/2*C rArr 3/2*C=9#

Sub.ing #3/2*C=9# in #(1)#, we get the complete Soln. - called The

Particular Soln. as #x^(3/2)+y^(3/2)=9#.