If `bx=ay` then show that `(x^2+y^2)(a^2+b^2)=(ax+by)^2`

If y= e^(ax) sin bx then show that, y_(2)- 2ay_(1) + (a^(2) + b^(2))y= 0

If x=a sin theta+b cos theta,y=a cos theta-b sin theta then show that (ax+by)^(2)+(bx-ay)^(2)=(a^(2)+b^(2))^(2)

Ifx=a sin theta+b cos theta,y=a cos theta-b sin theta then show that (ax+by)^(2)+(bx-ay)^(2)=(a^(2)+b^(2))^(2)

If x = cy + bz, y = az + cx , z =bx + ay, then prove that x^2/(1-a^2)= y^2/(1-b^2)

If y=e^(ax)sinbx show that y_2-2ay_1+(a^2+b^2)y=0 .

If x^3+y^3=3axy Show that dy/dx=(ay-x^2)/(y^2-ax) .

If y= e^(ax) sin(bx), show that y2 - 2ay1 + ( a^2 + b^2 ) y = 0

If y=e^(ax)sin bx, then prove that y_(2)-2ay_(1)+(a^(2)+b^(2))y=0

If y = e^(-ax) cos (bx + c) , show that (d^2y)/(dx^2) + 2a(dy)/(dx) + (a^2 + b^2) y = 0

(ax+by)^(2)+(bx-ay)^(2)