" 11."(d^(2)y)/(dx^(2))=x+sin x,quad " fall "quad (1)/(e)quad y=0,(dy)/(dx)=-1" afg "x=0

(d^(2)y)/(dx^(2))=x^(2)sin x, givenatx =0 if y=0,(dy)/(dx)=1

(d^(2)y)/(dx^(2))=(1)/(1+x^(2)) whenx =0,y=0 and (dy)/(dx)=0

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)(dy)/(dx)=x+y , iv) log_(e)(dy)/(dx)=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)(dy)/(dx)=x+y , iv) log_(e)(dy)/(dx)=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^((d^(3)y)/(dx^(3)))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)((dy)/(dx))=x+y , iv) log_(e)((dy)/(dx))=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

If e^(y)(x+1)=1, show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2) If y=sin(2sin^(-1)x), show that ((1-x^(2))d^(2y))/(dx^(2))=x(dy)/(dx)-4y

Solve: (d^2y)/dx^2=e^x(sinx+cosx) , given that y=1 and (dy)/(dx)=0 , when x=0

Solve: (d^2y)/dx^2=e^x(sinx+cosx) , given that y=1 and (dy)/(dx)=0 , when x=0

If y = sin^-1x , then show that (1-x^2)(d^2y)/(dx^2)- x dy/dx = 0

If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^(-1)x), show that ((1-x^2)d^(2y))/(dx^2)=x(dy)/(dx)-4y