4. If yet sin bx, prove that 32-2ay) + (a + b) y = 0. fam for

If y = e^[ax] sin bx , prove that d^2y/dx^2 - 2a dy/dx +(a^2 + b^2 ) y = 0 .

y=e^(ax)sin bx : Prove that y_2-2ay_1+(a^2+b^2)y=0 .

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

If y=e^(ax) sin bx then prove that (d^2y)/(dx^(2))-2a(dy)/(dx)+(a^(2)+b^(2))y=0 .

Solve: ax + by = a - b bx - ay = a + b

IF y=e^(ax)sin bx , then prove that, (d^2y)/(dx^2)-2ady/dx+(a^2+b^2)y=0

If x = cy + bz, y = az + cx,z = bx + ay where x,y,z are not all zero, prove that a^2 + b^2 + c^2 + 2ab = 1.

If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 and (2c+1) x + 2cy + c - a - b = 0 are concurrent , then the prove that either a+b+ c = 0 or (a+b+c)^(2) + 2a = 0