Integrate both sides again v = C1 4 x4 C2 Now the general solution is given as y2 = v(x)y1 y2 = ( C1 4 x4 C2)( 1 x) y2 = (C1( x3 4) C2( 1 x)) Now the first solution is given when C1 = 0, then the second solution can be when C2 = 0 which is x3 4 otherwise there are infinite solutionsby just filling the constants To checkMathx=s3t/math math\frac{d}{ds}x^2=\frac{d}{ds}(s3t)^2/math math=2(s3t)/math math\frac{d^2}{ds^2}x^2=\frac{d}{ds}(\frac{d}{ds}x^2)/math mathFunction equal to each other so there is no extra X or Y being consumed that gives no extra utility 2X=3Y rearrange Y=2X/3 – so ray from original which goes through all the corners of the L has to have the slope 2/3 The indifference curve is for when utility is 6 y 3 X 2 Ray from the origin slope is 2/3 U
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