- 微分方程式 解法集4 (differential equations 4)
- 難しい微分方程式解法集 (Hard), 初等関数で解ける難しーい微分方程式
- dy/dx +a/y =2bx, ... =-b/x^2
- d^2y/dx^2 +7dy/dx =4e^x
- (x^2 +x)d^2v/dx^2 +(x^2 +2x +1)dv/dx =0
- (x^2 -y^2) dy/dx =2xy
- dy/dx -2xy =2xe^x^2, dy/dx +tanx y =sinx
- d^2y/dt^2 +a(y^2 -1)dy/dt +y =0, y(t +Δt) =...
- d^2y/dx^2 +1/x dy/dx -ay =0
- d^2y/dx^2 =(dy/dx)^2 +1
- ∂u/∂t =a∂^2u/∂x^2 +b∂u/∂x +cu, ξ =x +b1 t, η=t, v =ue^(c1 η)
- (1 -xy) dy/dx =(x +y)y
- x dx/dt =-t
- dx/dt =x(1 -x) -h, (x =x0 +Δx)
- Hn =e^(-p(x)) d^n/dx^n e^p(x) --> e^(p(x +t) -p(x)) =Σ[n=0,∞] t^n /n! Hn(x)
- ∫ cosx/( (sinx)^2 -2sinx ) dx, ∫ 1/sinx dx, ∫ 1/( (cosx)^2 -(sinx)^2 ) dx, ∫ 1/(x^3 +1) dx
- F(s) =s/((s -2)^2 +1), F(s) =1/((s +1)(s +2)), dx/dt +2x =e^(-t)
- ∂u/∂t =a2 ∂^2u/∂x^2 +a0 u
- ∂u/∂x +∂u/∂y =0, u(0,y) =y^2
- x^2 d^2y/dx^2 -x(x +2)dy/dx +(x +2)y =f(x), 変数変換(y =e^f(x) z)
- x d^3y/dx^3 +3 d^2y/dx^2 =e^x, ∫ ∫ x^(-3) ∫ x^2 e^x dx dx dx
- df/dx =cot( f /(a -bx) )
- (2xy^4 e^y +2xy^3 +y)dx +(x^2 y^4 e^y -x^2 y^2 -3x)dy=0
- d^2x1/dt^2 =-dx1/dt -2x1 +0.5 dx2/dt +x2 +F cos(at), d^2x2/dt^2 =0.5 dx1/dt +x1 -0.5 dx2/dt -x2
- 空気振動(音波), 微分方程式, 2階線形微分方程式での変数変換
- dY/dt =AY +F(t,Y) --> e^(At) C + ∫[0,t] e^(A(t-s)) F(s,Y(s)) ds
- -y∂f/∂x +x∂f/∂y =0, x∂f/∂x +y∂f/∂y =2f
- x^dy/dx +y =0, (x +1) dy/dx =y +1
- m1 d^2 x1/dt^2 =f1 -f2, m2 d^2 x2/dt^2 =f2, f1 =-k1 x1, f2 =-k2 (x2 -x1)
- Mn d^2 Xn/dt^2 =Fn -F(n+1), F(n+1) =-k(X(n+1) -Xn)
- d^2y/dx^2 -6dy/dx +9y =xe^(2x), 5e^(2x)
- dy/dx =1/(2x +1) y^n, dy/dx +y/x =-7xy^2, (1/(cosx)^2 -cosy)dx +xsiny dy =0
- d^2x/dt^2 +adx/dt +bx =0, --> x0 =c1 x1 +c2 x2:一般解
- x^2 d^2y/dx^2 -xdy/dx +y =f(x)
- x(y -1)dy/dx =y, (cosx)^3 /(cosy)^2 dy/dx +2sinx =0, sqrt(1 +x)dy/dx =sqrt(1 +y)
- dy/dx -2y =x^2 e^(2x), 定数変化法は変数変換
- d^2y/dx^2 +y =f(x), d^2x/dt^2 +ω^2 x =f sin(ωt +φ)
- dy/dx +y =cos(2x), dy/dx =y(3 -y), dy/dt +ay =ku(t)
- t dx/dt =(t +1)x, x =Σ[n =0,∞] Cn...
- dy/dx =3y^(2/3)
- a2 d^2x/dt^2 +a1 x +a0(t) =0
- dy/dx =f(y,x), y(x +Δx) =(オイラー法、ホイン法、中点法), 後退オイラー法, 台形法, ルンゲクッタ法, ミルン法
- d^2y/dx^2 -2dy/dx =f(x), d^2x/dt^2 +2dx/dt =1
- 線形の微分方程式ではy =e^f(x) zが基本
- (x +1)dx +(y -1)dy =0, (x^2 -2xy -2y^2)dx +(y^2 -4xy -x^2)dy =0
- r d^2x/dt^2 =-r g +k dx/dt, r^3 =R^3 + ∫ [0,t] 3r^2 dx/du du
- ∂^2u/∂t^2 =c^2 ∂^2u/∂x^2, u(0,t) =0, ∂u/∂x|[x =L] =0, u(x,0) =u0 sin(π/(2L) x), ∂u/∂t|[t =0] =0
- k(1 +st1)/(1 +st2) 1/(1 +st3 +s^2 t4^2)
- d^3y/dx^3 -d^2y/dx^2 -dy/dx +y =e^x
- d^4y/dx^4 -2d^3y/dx^3 +d^2y/dx^2 =x^2
- dy1/dx =y1 -y2, dy2/dx =y1 +y2
- dx1/dt =x2, dx2/dt =2x1 +x2, ..., dx2/dt =-3x1 +4x2
- 2ds/dx +s +3dt/dx +t =0, ds/dx +s +dt/dx +2t =0
- P(y) dx +Q(x) dy =0, (y -1)dx +(x -3)dy =0, (x +f(y)) dy/dx +y +g(x) =0
- dy/dx +2xy =1 -x^2
- a' =F/m -a0
- d^2f/dx^2 =0, d^2g/dx^2 =a^2 (g -f)
- dx/dt =u (u <=0), dy/dt =v, (at -y)/x =v/(-u), u^2 +v^2 =b^2
- 境界条件の線形・同次
- d^2y1/dt^2 +cdy1/dt +4y1 -2y2 =0, d^2y2/dt^2 +cdy2/dt -2y1 +4y2 =0
- f(x,y) +f(1-x,1-y) =1, f(x,1/2) =x, f(1/2,y) =y
- Y =Kp (1 +1/(Ti s) +Td s /(1 +a Td s) ) E
- (x^2 -1) (dy/dx)^2 -2xydy/dx +y^2 =0
- bdy/dt =-k(y -x), adx/dt =G +k(y -x) -lx, 定数係数2階線形微分方程式, bdy/dt =.., dux/dt =G +k(y -x) -lx, du/dt =a
- y d^2y/dx^2 -(dy/dx)^2 =k y(y^2 -1)
- u =(xcosa -ysina) /(x^2 +y^2), v =(xsina +ycosa) /(x^2 +y^2), ∂u/∂x +∂v/∂y =?
- dy/dx -xy/(x^2 +1) =f(x)
- ∫ sqrt(1 -x^2) /(x +1)^2 dx
- ∂f/∂y -d/dx(∂f/∂y') =0, f(y,y') =(y +y0) sqrt(1 +y'^2)
- dy/dx =-y +sqrt(y^2 +ax), x dy/dx =y +a sqrt(x^2 +y^2)
- x(dy/dx +1) =tan(x +y)
- x∂u/∂x +(1 +y^2)∂u/∂y =0, u(x,0) =cosx
- y∂u/∂x -x∂u/∂y =0, u(x,0) =u0(x)
- d^2y/dt^2 -(1 -y^2)dy/dt =0: ルンゲクッタ
- d^2y/dx^2 +1/2 (dy/dx)^2 =2y
- P(x,y)∂u/dx +Q(x,y)∂u/dy =0
- Δy/Δt =func(t,y)
- ∂U/∂x -2U =e^(2x)
- ∂u/∂t =∂^2u/∂x^2, u(0,t) =u(L,t) =0, u(x,0) =sin(πx/L) -2sin(2πx/L)
- ∂^2u/∂r^2 +1/r ∂u/∂r +1/r^2 ∂^2u/∂θ^2, u(0,θ):有限
- A df/dx +Bf =C, ( A (sF -D) +B F =C/s )
- ∂u/∂t =4∂^2u/∂x^2, u(0,t) =u(2,t) =0, u(x,0) =sin(6πx)
- ∂^2u/∂t^2 =c^2 ∂^2u/∂x^2, ∂u/∂x|(x=0) =∂u/∂x|(x=2L) =0
- ∂^5v/∂x^4∂t +A∂^4v/∂x^4 +B∂v/∂t +Cv =0
- ∂z/∂x +∂z/∂y +z =0
- ΔA(t)/Δt =( M -aA(t) -bB(t) ) A(t), ΔB(t)/Δt =( N -cA(t) -dB(t) ) B(t)
- ∂u/∂t -∂u/∂x =0, u(x,0) =u0(x) --> 解法(qa8666919.html)
- ∂u/∂x +u∂u/∂y =0, u(0,y) =u0(y) =1 -y
- ∂u/∂t =∂^2u/∂x^2, u(0,t) =0, ∂u/∂x|(x=1) =0, u(0,t) =cost, u(∞,t)->0
- ∂u/∂t +c∂u/∂x =k∂^2u/∂x^2, u(0,t) =u(2π,t), u(x,0) =sinx
- おまけ:痛くない静電気対策
keywords
d^ : 2階以上
f(, "=e" : 非斉次
")^", "/(", /y, y^, ^3, e^, sin, cos : 非線形
", d" : 連立
∂ : 偏微分(方程式)
∫ : 積分(方程式) Δ : 数値解法
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Last updated
2022.06.28 13:30:41
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