1.Correct statement is/area.f(x,y)=x2ey/x+2x2(yx)+y2ln∣yx∣f(x, y) = x^2 e^{y/x} + 2x^2\left(\frac{y}{x}\right) + y^2 \ln\left|\frac{y}{x}\right|f(x,y)=x2ey/x+2x2(xy)+y2lnxy is a homogeneous function of degree two.b.f(x,y)=siny+xsin2y+xcosyf(x, y) = \frac{\sin y + x}{\sin 2y + x\cos y}f(x,y)=sin2y+xcosysiny+x is a homogeneous function of degree one.c.xsin(yx)dy+ysin(2yx)dx=0x\sin\left(\frac{y}{x}\right) dy + y\sin\left(\frac{2y}{x}\right) dx = 0xsin(xy)dy+ysin(x2y)dx=0 is a homogeneous differential equation.d.f(x,y)=ex/y+tan(yx)f(x, y) = e^{x/y} + \tan\left(\frac{y}{x}\right)f(x,y)=ex/y+tan(xy) is a homogeneous function of degree zero.Login to continueOnly logged in users canattempt or see the solution.
