The functions and satisfy the equation

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The functions u=exsin⁡xu=e^x\sin x and v=excos⁡xv=e^x\cos x satisfy the equation (1) vdudx−udvdx=u2+v2v\frac{du}{dx}-u\frac{dv}{dx}=u^2+v^2 (2) d2udx2=2v\frac{d^2u}{dx^2}=2v (3) d2vdx2=−2u\frac{d^2v}{dx^2}=-2u (4) All of these

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