High School
SAT
ACT
University
MCAT
LSAT
DAT

Solve the initial value problem f(x)=4x+(x^2)/2+5, F(1)=1/3

Related Topics

Wize University Calculus 1 Textbook > Integrals

Initial Conditions

3 Activities

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Solve the initial value problem
f(x)=4x+x22+5,F(1)=1/3\displaystyle f(x)=4x+\frac{x^2}{2}+5, F(1)=1/3
More Initial Conditions Questions:
Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Applications of Integration: Position, Velocity and Acceleration
If the accelertion of a particle is given by a(x)=2x+xa\left(x\right)=2^x+x, and v(0)=s(0)=0v\left(0\right)=s\left(0\right)=0, then the displacement of the particle s(x)s\left(x\right) is
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Practice: Indefinite Integral
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Practice: Indefinite Integral (~F2018 Final Q26)
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Exponential Functions: $f$ from $f''$
Given f′′(x)=5ex+2sin⁡xf''(x)=5e^x+2\sin x and given f(0)=0f(0)=0, f(π)=0f(\pi)=0, find f(x)f(x). Enter "f(x)=..."
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′′(x)=x2−2+sin⁡xf''\left(x\right)=x^2-2+\sin x, f(0)=3f\left(0\right)=3 and f′(3)=1f'(3)=1
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Applications of Integration: Position, Velocity and Acceleration
If the acceleartion of a particle is given by a(x)=2x+xa\left(x\right)=2^x+x, and v(0)=s(0)=0v\left(0\right)=s\left(0\right)=0, then the displacement of the particle s(x)s\left(x\right) is
Initial Conditions
Find the function y=f(x)y=f(x) if
y′′=3x−5/2y′(1)=1y(4)=6y''=3x^{-5/2} \quad y'(1)=1 \quad y(4)=6
Initial Conditions
Solve the initial value problem
y′=x2+1xy'=\frac{x^2+1}{\sqrt{x}}
y(1)=3y(1)=3
Initial Conditions
Solve the initial value problem
y′′=ex/2y′(0)=3y(0)=5y''=e^{x/2} \quad y'(0)=3 \quad y(0)=5
Initial Conditions
Find the function f(x)f(x) whose derivative is 4x−1/x24x-1/x^2 forx>0 x>0 and for which f(1)=−1f(1)=-1.
Solve the initial value problem
f(x)=x+x4x2,F(0)=2\displaystyle f(x)=\frac{\sqrt{x}+x^4}{x^2}, F(0)=2
Solve the initial value problem y′=sec⁡2x−e−x,    y(0)=2y'=\sec^2x-e^{-x},\ \ \ \ y\left(0\right)=2
Consider Newton's law of cooling dTdt=2−T10\displaystyle\frac{\text{d}T}{\text{d}t}=2-\frac{T}{10} . Determine T(t)T(t) if T(0)=100T(0)=100
Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Practice: Rearrange First
Q:\bf{Q:} Solve the initial value problem t2dydt+1=t3t^2\dfrac{dy}{dt} + 1 = t^3 with y(1)=1y(1) = 1
Q:\bf{Q:} Solve the initial value problem y′=x3+sin⁡2xy'=x^3+\sin2x given y(π2)=0y\left(\dfrac{\pi}{2}\right)=0
Q:\bf{Q:}Solve the initial value problem y′=sec⁡2x−e−xy'=\sec^2x-e^{-x} with y(0)=2y\left(0\right)=2
Solve the initial-value problem
y′=x2+1xy(1)=3\begin{aligned} y' &=\dfrac{x^2 + 1}{\sqrt{x}}\\ y(1) & = 3 \end{aligned}
Practice: From Second Derivative to Function
Q:\bf{Q:} Solve the initial-value problem y′′=sin⁡2xy'' = \sin 2x, y′(0)=3y'(0) = 3 , y(0)=5y(0) = 5.
Exponential Functions: $f$ from $f''$
Given f′′(x)=5ex+2sin⁡xf''(x)=5e^x+2\sin x and given f(0)=0f(0)=0, f(π)=0f(\pi)=0, find f(x)f(x). Enter "f(x)=..."
Solve the initial value problem
y′′=ex/2y′(0)=3y(0)=5\begin{aligned} y''& = e^{x/2}\\ y'(0)& = 3\\ y(0) &= 5 \end{aligned}
Solve the initial value problem y′=sec⁡2x−e−x,  y(0)=2y'=\sec^2x-e^{-x},\ \ y\left(0\right)=2.
Practice: Indefinite Integral
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Find the antiderivative FF
f(x)=x+x4x2,F(1)=2\displaystyle f(x)=\frac{\sqrt{x}+x^4}{x^2}, F(1)=2
Find the antiderivative FF
f(x)=4x+x22+5,F(1)=1/3\displaystyle f(x)=4x+\frac{x^2}{2}+5, F(1)=1/3