Category: 0. BLOG

Find order and degree ofleft(y′′′right)4+(y′′)3=0left(y′′′right)4+(y′′)3=0 A Order 4, Degree 3 B Order 3, Degree 4 C Order 3, Degree 3

Find order and degree of y′′′+(y′)4=0y′′′+(y′)4=0 A Order 1, Degree 4 B Order 4, Degree 3 C Order 3, Degree

Find order and degree of (y′′)3+y′=0(y′′)3+y′=0 A Order 3, Degree 2 B Order 2, Degree 1 C Order 2, Degree

Which part decides the order of a differential equation A Highest derivative order B Highest power only C Number of

Which statement best defines a differential equation A Equation with limits B Equation with derivatives C Equation with vectors D

Evaluate ∫01×31+x2 dx∫011+x2x3dx using a smart algebraic split before integrating. A 12+12ln⁡221+21ln2 B 12−12ln⁡221−21ln2 C ln⁡2−12ln2−21 D 14ln⁡241ln2 Explanation Write x31+x2=x−x1+x21+x2x3=x−1+x2x.

Evaluate ∫4x(1+2×2) dx∫(1+2×2)4xdx using a suitable substitution. A ln⁡(1+2×2)+Cln(1+2×2)+C B ln⁡∣x∣+Cln∣x∣+C C 12ln⁡(1+2×2)+C21ln(1+2×2)+C D 14ln⁡(1+2×2)+C41ln(1+2×2)+C Explanation Let u=1+2x2u=1+2×2. Then du=4x dxdu=4xdx. So

A function f(x)f(x) satisfies f′(x)=2x(1+x2)4f′(x)=2x(1+x2)4. What is ∫2x(1+x2)4 dx∫2x(1+x2)4dx? A (1+x2)55+C5(1+x2)5+C B (1+x2)5+C(1+x2)5+C C 2x(1+x2)4+C2x(1+x2)4+C D (1+x2)44+C4(1+x2)4+C Explanation Use substitution u=1+x2u=1+x2,

When you see ∫f′(x) f(x) dx∫f′(x)f(x)dx, which method is usually simplest to start with? A By parts method B Partial fractions C

Which statement best defines an antiderivative of f(x)f(x)? A Function is constant B Integral equals zero C Derivative equals f(x)f(x)