Question: Solue the following Cauchy problem: Xy Uk + y uy + yu = y-x with us y= x? on 2 solve the Following Ca

Solue the following Cauchy problem: Xy Uk + y" uy + yu = y-x with us y= x? on 2 solve the Following Ca
uchy prob. x y u +y*uy +yu - y- x with u-
y = x2 1-C () dy du dx xy y -x yu

Solue the following Cauchy problem: Xy Uk + y" uy + yu = y-x with us y= x? on 2 solve the Following Ca uchy prob. x y u +y*uy +yu - y- x with u- y = x2 1-C () dy du dx xy y -x yu + CL dy de dy 3D log x - log y + log C. - dy du y-- yu du dg y-X-yu %3D dy - G -) dy du 1-G dy dy du 1-Ci dy y2 the example... Ex: @ Find a . goneral Solution to Ux +2 x2 Uy x2 ex Find partiCular solution Satisfying the Cauchy data on the giwen Curues: O ulx yl=X ulx.y)=x on Oulxy)=X on yax2+2 yaxex dy 2x2 du x2 ex +u dx dy dy 2x dx 2x2 x2 + C. x du xe+u dx dx du x2 ex +4 dintar eg dx I. F: du dx X2 dx +Cq g(y-x2). i the general solution is ucx.y)-x+ X gl4-x3) DucX,y)-x on + X = x gril=l-ex nat passible %3D %3D No solution for thir Case

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