Determine the order and degree of the differential equation \(2x\frac{d^4y}{dx^4}+5x^2(\frac{dy}{dx})^3-xy=0\)
AFourth order, first degree
BThird order, first degree
CFirst order, fourth degree
DFirst order, third degree
Mathematics · Question Bank
Differential Equations
15 of 42 questions match. Answer in your head first, then check the solution.
Which of the following equations is an exact DE?
A\((x^2+1)dx-xy\,dy=0\)
B\(x\,dy+(3x-2y)dx=0\)
C\(2xy\,dx+(2+x^2)dy=0\)
D\(x^2y\,dy-y\,dx=0\)
Which of the following equations is a variable separable DE?
A\((x+x^2y)dy=(2x+xy^2)dx\)
B\((x+y)dx-2y\,dy=0\)
C\(2y\,dx=(x^2+1)dy\)
D\(y^2dx+(2x-3y)dy=0\)
Find the equation of the curve at every point of which the tangent line has a slope of \(2x\).
A\(x=-y^2+C\)
B\(y=-x^2+C\)
C\(y=x^2+C\)
D\(x=y^2+C\)
What is the solution of the first order differential equation \(y(k+1)=y(k)+5\)?
A\(y(k)=4-\frac{5}{k}\)
B\(y(k)=20+5k\)
C\(y(k)=C-k\), where C is constant
DThe solution is non-existent for real values of y
Find the differential equations of the family of lines passing through the origin.
A\(y\,dx-x\,dy=0\)
B\(x\,dy-y\,dx=0\)
C\(x\,dx+y\,dy=0\)
D\(y\,dx+x\,dy=0\)
What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis.
A\(2x\,dy-y\,dx=0\)
B\(x\,dy+y\,dx=0\)
C\(2y\,dx-x\,dy=0\)
D\(\frac{dy}{dx}-x=0\)
Determine the differential equation of the family of lines passing through \((h,k)\).
A\((y-k)dx-(x-h)dy=0\)
B\((y-h)+(y-k)=\frac{dy}{dx}\)
C\((x-h)dx-(y-k)dy=0\)
D\((x+h)dx-(y-k)dy=0\)
The equation \(y^2 = cx\) is the general solution of:
A\(y' = \dfrac{2y}{x}\)
B\(y' = \dfrac{2x}{y}\)
C\(y' = \dfrac{y}{2x}\)
D\(y' = \dfrac{x}{2y}\)
A certain radioactive substance has a half-life of 3 years. If 10 grams are present initially, how much of the substance remains after 9 years?
A1.50 grams
B1.25 grams
C2.50 grams
D1.75 grams
Find A for which \(y = Ae^x\) will satisfy \(y'' - 2y' = 4e^x\).
A−1
B−2
C−3
D−4
Find the general solution of \(y' + \dfrac{x}{y} = 0\).
A\(x^2 + 2y^2 = C\)
B\(x^2 + y^2 = C\)
C\(x^2 - 2y^2 = C\)
D\(x^2 - y^2 = C\)
The equation \(y^2 = cx\) is the general solution of
A\(y' = \dfrac{2y}{x}\)
B\(y' = \dfrac{2x}{y}\)
C\(y' = \dfrac{y}{2x}\)
D\(y' = \dfrac{x}{2y}\)
Solve the differential equation \(y' = \dfrac{y}{2x}\).
Ay = cx
By² = cx
Cy = cx²
Dy³ = cx
A laboratory has a 75-gram sample of radioactive material. The half-life of the material is 10 days. What is the mass of the laboratory’s sample remaining after 30 days?
A9.375 grams
B11.25 grams
C12.5 grams
D22.5 grams