`y=xe^(x^(2))` Find `y^(prime prime)`.

The differential equation of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=C is a. y^(primeprime)/y^(prime)+y^(prime)/y-1/x=0 b. y^(primeprime)/y^(prime)+y^(prime)/y+1/x=0 c. y^(primeprime)/y^(prime)-y^(prime)/y-1/x=0 d. none of these

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? y^(x-2x y^(prime))=y y y^(prime)=2x(y^(prime))^2+1 x y^(prime)=2y(y^(prime))^2+2 y^(y-4x y^(prime))=(y^(prime))^2

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally

If y=f((2x-1)/(x^2+1)) and f^(prime)(x)=sinx^2 , find (dy)/(dx) .

Consider the family of all circles whose centers lie on the straight line y=x . If this family of circles is represented by the differential equation P y^(primeprime)+Q y^(prime)+1=0, where P ,Q are functions of x , y and y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)), then which of the following statements is (are) true? (a)P=y+x (b)P=y-x (c)P+Q=1-x+y+y^(prime)+(y^(prime))^2 (d)P-Q=x+y-y^(prime)-(y^(prime))^2

Consider the family of all circles whose centers lie on the straight line y=x . If this family of circles is represented by the differential equation P y^(primeprime)+Q y^(prime)+1=0, where P ,Q are functions of x , y and y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)), then which of the following statements is (are) true? (a) P=y+x (b) P=y-x (c) P+Q=1-x+y+y^(prime)+(y^(prime))^2 (d) P-Q=x+y-y^(prime)-(y^(prime))^2

If (a x^2+c)y+(a^(prime)x^2+c^(prime) )=0 and x is a rational function of y and ac is negative, then a. a c^(prime)+c^(prime)c=0 b. a//a '=c//c ' c. a^2+c^2=a^('2)+c^('2) d. a a^(prime)+c c^(prime)=1

If (a x^2+c)y+(a^(prime)x^2+c^(prime) )=0 and x is a rational function of y and ac is negative, then a. a c^(prime)+c^(prime)c=0 b. a//a '=c//c ' c. a^2+c^2=a^('2)+c^('2) d. a a^(prime)+c c^(prime)=1

The two lines a x+b y=c and a^(prime) x+b^(prime) y=c^(') are perpendicular if